1. Field of the Invention
This invention relates to a technique of easily and quickly determining the optimum value of feedback gain used for calculating correction amount in feedback control.
2. Description of the Prior Art
Feedback control is frequently adopted for, for instance, moving an automatic guidance vehicle along a predetermined course. The control comprises a step of detecting a deviation or error .DELTA.E from the course, a step of calculating correction amount according to the detected error .DELTA.E, and a step of correcting the steering angle of the vehicle according to the calculated correction amount, these steps being executed repeatedly.
Generally, in the feedback control, the correction amount is calculated in any of the following ways:
P system: A value (P.times..DELTA.E) which is proportional to the error is used as the correction amount.
PI system: The sum of a value proportional to the error and a value proportional to an integral of the error (P.times..DELTA.E+I.times.integral of .DELTA.E) is used as the correction amount.
PD system: The sum of a value proportional to the error and a value proportional to a differential of the error (P.times..DELTA.E+D.times.differential of .DELTA.E) is used as the correction amount.
PID system: The sum of a value proportional to the error, a value proportional to an integral of the error and a value proportional to a differential of the error (P.times..DELTA.E+I.times.integral of .DELTA.E+D.times.differential of .DELTA.E) is used as the correction amount.
The factors P, I and D as used in the above formula are feedback gains. Specifically, the P gain is a proportional gain, the I gain is an integral gain, and the D gain is a differential gain. The values of the feedback gains such as the P, I and D gains have great influence on the feedback control characteristics. For example, if the P or proportional gain is too small in value, the correction of the running course of the automatic guidance vehicle is delayed. If the gain is too large, on the other hand, the running course meanders greatly.
Accordingly, on-site processes have heretofore been contemplated, which permit the optimum value of feedback gain to be found out easily and in a short period of time. A typical one of such processes is a limit sensitivity process which is disclosed in ASME trans., vol. 64, (1942. 11.), J. G. Ziegler, N. B. Nichols, pp. 759-768.
In this limit sensitivity process, the magnitude of the P gain with which the error is undergoing self-sustaining vibration is obtained by carrying out actual feedback control on the subject of control, and the optimum value of each gain is determined from the value of the P gain at this time in accordance with experiment rules.
Specifically, the I and D gains are set to zero, that is, the sole P gain is made variable in a trial feedback control, and the P gain is increased gradually. When the self-sustaining vibration of the error is obtained, the P, I and D gains are set to be, for instance:
P gain=0.6.times.P.sub.c PA1 I gain=0.5.times..tau..sub.c PA1 D gain=0.125.times..tau..sub.c
where P.sub.c is the value of the P gain at this time and .tau..sub.c is the period of the self-sustaining vibration.
In these formulas, the individual coefficients are obtained experimentally, and their adequacy empirically verified. In this way, the values of the P, I and D gains are determined.
In the limit sensitivity process, however, problems are encountered in the practical way of detecting the self-sustaining vibration. Besides, depending on the subject of control, there may be cases when it is difficult to detect the reaching of the state of the self-sustaining vibration.
As an example, in the feedback control for moving an automatic guidance vehicle (hereinafter referred to as AGV) along a course, it is not easy to accurately determine the instant of reaching of the self-sustaining vibration because of very slow changes in the course of the AGV.